Question

Assertion: The system of three linear equations in three unknown variables can be written in the matrix form as AX = B. It has a unique solution X = A⁻¹B.

Reason: Matrix A is non-singular.

Options

• Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

• Assertion is true and Reason is false.

• Assertion is false and Reason is true.

Answer 1

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Explanation:

A system of linear equations has a unique solution only when the inverse of matrix A exists. In that case, the solution is given by X = A⁻¹ B. The inverse A⁻¹ exists only when matrix A is non-singular. Hence, the reason correctly explains the assertion.